Computer Science
In the following truth table x and y are inputs and B and D are outputs:
| Input | Output | ||
|---|---|---|---|
| x | y | B | D |
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 0 | 0 |
Answer the following questions:
(i) Write the SOP expression for D.
(ii) Write the POS expression for B
Boolean Algebra
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Answer
(i) Write the SOP expression for D.
| x | y | D | Min Terms |
|---|---|---|---|
| 0 | 0 | 0 | |
| 0 | 1 | 1 | x'y |
| 1 | 0 | 1 | xy' |
| 1 | 1 | 0 |
SOP expression = x'y + xy'
(ii) Write the POS expression for B
| x | y | B | Max Terms |
|---|---|---|---|
| 0 | 0 | 0 | x+y |
| 0 | 1 | 1 | |
| 1 | 0 | 0 | x'+y |
| 1 | 1 | 0 | x'+y' |
POS expression = (x+y).(x'+y).(x'+y')
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